The hei of Avraham binds creation to Hashem

בפסוק והיה שמך אברהם.

On the verse, "And your name shall be Avraham" (Bereishis 17:5).

The Sefas Emes examines the moment Hashem changes Avram's name to Avraham by adding the letter hei.

דרשו חז"ל שניתוסף לו ה' להיות שליט על כל רמ"ח איברים.

Chazal expounded that the letter hei was added to him to be a ruler over all 248 limbs.

The added hei gave Avraham mastery over all 248 of his limbs (corresponding to the 248 positive mitzvos), making his whole body subject to the service of Hashem.

דאיתא בהבראם בה' בראם בה' נברא עוה"ז כו'.

For it is taught: "When they were created" (be'hibaram) — read as "with hei He created them" (be'hei beraam); with the letter hei this world was created.

Chazal read the word be'hibaram as an anagram, teaching that Hashem created this physical world with the letter hei — the same letter now added to Avraham's name.

עוד איתא באברהם.

Further it is taught regarding Avraham.

He brings an additional teaching about Avraham's special role in creation.

דהנה אמרו חז"ל שאברהם אבינו הקנה להקב"ה שמים וארץ והוא אחד מחמשה קנינים שקנה הקב"ה בעולמו.

For Chazal said that Avraham Avinu caused the Holy One, blessed be He, to acquire heaven and earth, and this is one of the five acquisitions (kinyanim) that Hashem acquired in His world.

By proclaiming Hashem as Master of heaven and earth, Avraham "acquired" them for Hashem — counted by Chazal as one of the five precious kinyanim in the world (Avos 6:10).

דאיתא כל מה שברא הקב"ה לא בראו אלא לכבודו דכתיב כל הנקרא בשמי ולכבודי בראתיו.

For it is taught: Everything that Hashem created, He created only for His glory, as it is written, "Everyone that is called by My name, I created him for My glory" (Yeshayahu 43:7).

The entire purpose of creation is to reveal the kavod (glory) of Hashem, as the navi states explicitly.

וזה הכבוד נתקיים ע"י הצדיקים דכ' ויקרא אברם בשם ה' והיינו דביקות הבריאה בהבורא ית' כדברי המדרש שאיחה את העולם כו'.

And this glory is fulfilled through the tzaddikim, as it is written, "And Avram called out in the name of Hashem" (Bereishis 12:8); and this is the attachment of creation to its Creator, may He be blessed, as the Midrash says, that he stitched the world together.

The tzaddik realizes creation's purpose by calling out and attaching the world back to its Creator. Avraham "stitched together" (icha) the seam between the world and Hashem, binding the two in deveikus (cleaving).

ונתקיים כל הנקרא בשמי וחל ש"ש על הבריאה בכח עבודת אאע"ה וזה רמז הה' שניתוסף לו.

And "everyone that is called by My name" was fulfilled, and the Name of Heaven rested upon creation through the power of the avodah of Avraham Avinu — and this is what the added hei alludes to.

Through Avraham's avodah, Hashem's Name came to rest upon the created world; the hei added to his name signifies this very power to draw the Divine Name onto creation.

וכביכול הניח הקב"ה ה' אברים להיות ברשותו שהמה עדות על הבורא ית'.

And, as it were, Hashem left five limbs in man's own domain, which serve as testimony to the Creator, may He be blessed.

Hashem entrusted to man's free choice certain organs (the "five" alluded to by the hei) so that man's voluntary service of Hashem with them bears witness to the Creator.

וכשהאדם משעבד כל האיברים שהם בבחירתו אז הקב"ה מוסיף לרשותו ה' איברים הללו ג"כ וחל שם ה' שהוא הה' שברא בה העוה"ז וזה רמז הה' קנינים שקנה בעולמו:

And when a person subjugates all the limbs that are within his free choice, then Hashem adds to his domain these five limbs as well, and the Name of Hashem rests upon him — which is the hei with which He created this world; and this is the allusion of the five kinyanim that He acquired in His world.

When a person presses all his free-willed organs into Hashem's service, Hashem grants him mastery over even more — and the Divine Name (the creative hei) rests upon him. This is the inner meaning of the five kinyanim: through such avodah, like Avraham's, a person becomes one of Hashem's treasured acquisitions in the world.

Summary: The Sefas Emes explains the hei added to Avraham's name as the very letter with which Hashem created this world. Through his avodah, Avraham bound creation back to its Creator and caused Hashem's Name to rest upon the world. When a person subjugates all the limbs given to his free will, Hashem extends his domain and rests His creative Name upon him — the deeper meaning of the five kinyanim Hashem acquired in His world.